Chapter 3 Copula-VAR Analysis of the Relation between … · Copula-VAR Analysis of the Relation between GDP, Imports, Exports: ASEAN Case ... and AEC considers the following key

Chapter 3

Copula-VAR Analysis of the Relation between GDP,

Imports, Exports: ASEAN Case

Warattaya Chinnakum1 and Songsak Sriboonchitta 2

1 Faculty of Economics ,Chiang Mai University

E-mail: [email protected]

2 Faculty of Economics ,Chiang Mai University

E-mail: [email protected]

This study concentrates on the causal relationship among output, imports, and

exports in ASEAN economies for the period 1980–2010. The investigation is

conducted in a time series framework using a vector autoregressive model with

copula approach, and impulse response function to test the trade variables of

exports and imports for exogenous or endogenous induced growth. Moreover,

results suggest there is no causal relation among imports, exports, and output in

Malaysia, Thailand, and Brunei. In contrast, the study found empirical evidence

in support of bi-directional causal relationship between exports and GDP growth

for Laos and The Philippines. Furthermore, the results of Indonesia, Singapore,

and Vietnam support only ELG hypothesis, not GLE hypothesis. Empirical

results also suggest that there is evidence in support of ILG hypothesis for The

Philippines, Indonesia, Singapore, and Vietnam. Thus, it is reasonable to

conclude that for several ASEAN countries, both exports and imports play a very

important role in stimulating economic growth.

34 Chapter 3 W. Chinnakum and S. Sriboonchitta

1. Introduction

International trade is often considered to be a main determinant of economic

growth in several countries, especially the Association of Southeast Asian Nations, or

ASEAN, countries, for which their growth rate of exports and imports have been grown

faster and higher than their GDP growth during the past thirty years. Table 1 shows

evidence that export growth and import growth are more than GDP growth from 1990 to

2010 in the ASEAN countries (except Vietnam, Laos, Thailand, and Cambodia in

1990), which implies that exports and imports could be main factors to determine output

in the ASEAN economies. Table 1 also shows the trend of export growth and import

growth. Export growth in ASEAN has continually increased since 1990 in most

countries, which arises from export-oriented market-based policies and free trade area

agreements. Moreover, import growths also increased from 1990 to 2010, and were

mainly due to imports of raw materials, capital goods, and machinery to produce for

domestic and exports sector. Furthermore, in 2015, ASEAN aims to integrate ten

countries to be one regional economic community called the ASEAN Economic

Community (AEC), and AEC considers the following key characteristics: (a) a single

market and production base, (b) a highly competitive economic region, (c) a region of

equitable economic development, and (d) a region fully integrated into the global

economy (ASEAN (2012)). This mean the economic integration will encourage trade in

the ASEAN countries and could be lead to increases in GDP in the future.

Therefore, the primary purpose of this study is to investigate the relationship

between trade and economic growth in the ASEAN countries which is important for

policymakers and governments in the ASEAN countries to decide direction or

appropriate policy for trade in their countries, and to decide whether the policies should

be the same or different in each country after economic integration.

Moreover, in recent years, many research projects have studied the relationship

between trade and economic growth, and a large volume of empirical research has

confirmed that trade is crucial and necessary for growth and development (Kababie

(2010)). However, most studies are interested only in exports factor and attempt to test

two hypotheses, which are Exports Lead Growth and Growth Lead Exports, but ignore

the imports factor. Reizman, Summers, and Whiteman (1996) argued that exports are

not only one factor to determine growth, but imports are also important, and the result

will be incomplete and spurious if analyzing a system without including imports. In

addition, Awokuse (2008) states that exports in some countries are not an important

engine or condition to drive the economy, and Kababie (2010) has established that

imports are valuable to economic growth for three primary reasons: (1) they are a source

of technology transfers; (2) they promote innovation through imports competition; and

(3) they provide factors of production, which are used in both domestic and export

sectors.

Asian Economic Reconstruction and Development under New Challenges 35

TABLE 1. GDP growth, Exports growth, and Imports growth of 10 ASEAN countries

from 1990-2010.

Country 1990 2000 2010

GDP

growth

Exports

growth

Imports

growth

GDP

growth

Exports

growth

Imports

growth

GDP

growth

Exports

growth

Imports

growth

Brunei 20.95 17.51 16.50 0.54 23.90 7.49 17.26 28.06 22.86

Vietnam 2.84 2.12 -6.27 8.62 25.49 33.16 11.17 22.07 19.18

Malaysia 13.34 17.44 29.15 16.73 16.09 25.50 23.25 26.45 33.13

Indonesia 12.79 17.07 33.61 17.87 27.67 39.63 31.49 35.43 39.93

The

Philippines 3.82 5.69 16.33 -2.38 7.70 12.12 18.46 30.64 19.27

Singapore 23.66 17.96 22.67 11.11 20.37 21.21 22.49 30.50 26.37

Thailand 18.53 14.28 31.69 0.08 17.90 22.99 20.93 28.55 36.91

Lao PDR 19.30 -32.44 15.43 15.33 -15.40 -14.72 15.42 44.37 23.61

Cambodia 159.83 101.25 8.00 4.13 7.95 14.61 8.08 11.84 25.55

Myanmar N/A N/A N/A 4.93 42.13 20.26 28.83 9.96 40.60

Source: IMF (2012)

Note: N/A = data are not available

Therefore, this study investigates the causal relationship among exports, imports,

and economic growth for the ASEAN economies within an integrated concept that

investigates the role of both exports and imports. The contributions of this paper are the

following: 1) export growth and import growth are included in the model as endogenous

variables which previous empirical studies specify as exogenous variables. 2) We

employ copula-VAR model (suggested by Bianchi, et. al (2010)). The advantage of

copula approach is to build flexible multivariate distributions and to consist in

representing the joint probability distribution by separating the impact of the marginals

from the association structure, explained by the copula functional form. Moreover, there

are no empirical studies using copula-VAR model to investigate causality among

exports, imports, and GDP.

The rest of this article is organized as follows: Section 2 provides a brief

empirical overview of the exports, imports, and output growth relationship. Section 3

discusses the analytical framework and some methodological issues. Section 4 presents

empirical findings, and Section 5 contains the concluding remarks.

2. Literature review

The role of exports and imports in promoting growth is perhaps the most

discussed topic as far as the role of trade in the economy is concerned. Although there

are vast empirical studies that emphasize the positive relationship between trade and

economics, Rodriguez and Rodrik (1999) highlight that the controversy between the

relationship of trade and economic growth has yet to be resolved. They mention the

problem of endogenous relations between income and trade. For example, recent studies

have observed that countries with high incomes tends to trade more, and when the trade


(especially exports) rises, the income also increases. Therefore, to consider only one

direction from trade to economic growth will lead to incomplete results.

According to Awokuse (2008), there are three dominant hypotheses proposed to

the economic literature: 1) Export-Led Growth (ELG), 2) Growth-Led Export (GLE),

and 3) Imports-Led Growth (ILG). Of the three hypotheses, most empirical testing has

been carried out on the ELG and GLE. However, the empirical evidence on the

relationship among exports growth, imports growth, and GDP growth is rather mixed,

and the results of different regions or countries in different periods of time provide

different conclusions.

Several pieces of empirical evidence on the ELG hypothesis have shown that

there is a link between economic growth and export growth. But debates still surround

the direction of causality. While some researchers have found evidence in support of the

ELG hypothesis (Ramos (2001), Sato and Fukushige (2011)), others (Reppas and

Christopoulos (2005)) either found reverse causal flow from economic growth to

exports growth, or support the alternative GLE hypothesis. Moreover, in some cases, the

empirical evidence indicated a bi-directional causal relationship (Khan, et al. (1995),

Zang and Balmbridge (2012)).

Moreover, on the context of ILG, endogenous growth models show that imports

can be a channel for long-run economic growth because it provides domestic firms with

access to needed intermediate factors and foreign technology (Coe and Helpman, 1995).

Thangavelu and Rajaguru (2004) found that there is no export-led productivity growth

for Hong Kong, Indonesia, Japan, Taiwan, or Thailand. However, significant causal

effects were found from imports to productivity growth in India, Indonesia, Malaysia,

The Philippines, Singapore, and Taiwan, which similarly result as Marwah and Tavakoli

(2004) who consider the effect of foreign direct investment (FDI) and imports on

economic growth in four Asian countries (Indonesia, Malaysia, The Philippines, and

Thailand) and the result shows FDI and imports are important factors to determine

economic growth. In Awokuse (2008), they suggest that economic growth could be

driven primarily by growth in imports, and Çetinkaya and Erdoğan (2010) also found

imports influenced GDP in Turkey. Pistoresi and Rinaldi (2012) found exports were not

the only or the main driver of economic growth in Italy from1863 to 2004.

3. Methodology

This article attempts to capture the causality among exports, imports and GDP

via the vector autoregressive (VAR) framework of Sims (1980). Moreover, traditional

approach assumed the joint distribution of error term is normality. However, Bianchi

et.al (2010) proposes to use of copula to construct the joint distribution and their result

show that the copula-Vector Autoregression (VAR) model outperforms or at worst

compares similarly to normal VAR models, keeping the same computational tractability

of the latter approach. Therefore, in our paper, we employ copula approach to construct

VAR model and compare with normal VAR model. This section provides a brief

discussion of the copula-VAR model adopted in this study. Since the vector


autoregressive (VAR) is fairly commonplace and well-document elsewhere, only a brief

overview is provided here.

Let ),...,,( 21 ntttt yyyY denote an )1( n vector of n endogenous variables. The

general p-lag vector autoregressive ))(( pVAR model has the form

TthYYYcY tptpttt ,...,1,...2211 (1)

where i are )( nn coefficient matrices and t is standard innovation which

has an )1( n unobservable zero mean and variance one.

Moreover, their conditional joint distribution is );,...,( ,,1 tnttH with the

correlation parameters vector . From the Sklar Theorem (1959), the joint distribution

can be written in the copula as

:):(),...,:();,...,( ,1,11,,1 ntnnttntt FFCH (2)

where ):( , itiiF is marginal distribution functions of ti , with marginal

parameter i and :C is the copula function which copula parameter . A copula is a

function that links together univariate distribution functions to form a multivariate

distribution function. Joe (1997) and Nelsen (2006) provide a complete monograph of

an introduction to the theory of copulas and a large selection of related models. Another

reviews such as Frees and Valdez (1998) and Cherubini et al. (2004) provide more

detail about the application in actuarial and financial settings.

From (2) the expression of the corresponding densities can be derived. By taking

derivatives to equation (2) we have:

),...,( 1 nf =

n

n

n H

1

1 ,, =

n

nn

n FFC

1

11 ,,

=

n

i i

ii

nn

nn

n

d

dF

FF

FFC

111

11 ,,

=

n

i

iinn fFFc1

11 ,, (3)

From inverse Sklar’s theorem which provide

nuuC ,,1 = nn uFuFF 1

1

1

1 ,, (4)

where niuFFu iiiiii ,...,2,1,1 .

Therefore, equation (4) becomes:


nuuc ,,1 =

n

i

iii

nn

uFf

uFuFf

1

1

1

1

1

1 ,, (5)

where nuuc ,,1 is the multivariate copula density.

By using equation (5), we can derive the Normal-copula, whose probability

distribution and density function is:

n

G uuC ,,1 =

:,, 1

1

1

nuu (6)

and

n

G uuc ,,1 =

n

i

ii

n

u

uu

1

1

1

1

1 ,,

(7)

where 1 is the univariate Gaussian inverse distribution function

( iiiu ,while is the correlation matrix.

Moreover, there are alternative copula families which are called Archimedean

copulas (such as Clayton's copula ,Rotated Clayton copula, Plackett copula, Frank

copula, Gumbel copula, Rotated Gumbel copula and Symmetries Joe-Clayton copula)

are provided to model the joint distribution. However, these copulas can become

inflexible in high-dimensions and do not allow for different dependency structure

between pairs of variables.

Moreover, Aas et.al(2009) presented a method to build high dimension copulas

using pair-copulas as building blocks and they show that the pair-copula decomposition

treated in their studies are more flexible to build higher dimension copula. This

decompositions are called vine copulas. Initially proposed by Joe (1996) and developed

in more detail in Bedford and Cooke (2001, 2002) ,Kurowicka and Cooke(2006) and

Brechmann ans Schepsmeirer (2011), vines are a flexible graphical model for describing

multivariate copulas built up using a cascade of bivariate copulas, so-called pair-

copulas. According to Aas, et.al(2009) ,they described statistical inference techniques

for the two classes of canonical (C-) and D-vines. Moreover, in this study, we provide

C-vines copula in 3-dimensions and the tree of C-vine show as Figure 1


T1

T2

Figure 1. A canonical vine with 3 variables ,2 trees and 3 edges.

The general expression for the canonical structure in the 3-dimensions case is

),,( 321 f = 32232112321 ,,)()()( FFcFFcfff

1312123, FFc (8)

or in the n-dimensions case we can write the general expression as follow:

n

i

n

i

in

j

ijiiijiiiijiiii FFcff1

1

1 1

)1(:1,1111)1(:1,,,(),,,()()(

(9)

where nif i ,...,1, denote the marginal densities and )1(:1, ijii

c bivariate copula

densities with parameter(s) )1(:1, ijii

.

The crucial question for inference is how to obtain the conditional distribution

functions F for an m-dimensional vector . For a pair-copula term in tree m+1,

this can easily be established using the pair-copulas by sequentially applying the

relationship

jj

jjjv

F

FFCFh

jj

,

, (10)

where j is an arbitrary component of and j denotes the ( 1m )-

dimensional vector excluding j (Joe 1996). Further jj v

C

is a bivariate copula

23/1

13

12

1

2

3

12 13


distribution function with parameter(s) specified in tree m . The notation of the h -

function is introduced for convenience (cp. Aas et al. 2009).

Copula and marginal estimation

The estimate the mariginal and copula parameter, Bianchi (2010) provided

multi-step procedure is known as the method of Inference Functions for Margins (IFM).

According to the IFM method, the parameters of marginal distributions are estimated

separately from the parameters of the copula. The estimation following two steps:

(1) Estimate the parameters nii ,...,1, of the marginal distributions iF using

the Maximum Likelihood (ML) method:

);(logmaxarg)(maxargˆ1

,

T

t

itiii

i

i fl (11)

where il is the log-likelihood function of the marginal distribution iF ;

(2) Estimate the copula parameters , given the estimations performed in Step

1:

T

t

ntnnt

c FFcl1

,1,11 ;ˆ;,...,ˆ;logmaxarg)(maxargˆ (12)

where cl is the log-likelihood function of the copula.

4. Empirical Analysis and Results

4.1 Data and unit root properties

Data was obtained for eight ASEAN countries1: Brunei, Vietnam, Malaysia,

Indonesia, Philippines, Singapore, Thailand and Laos. The data set consists of

observations for GDP growth (GDP), exports growth (EXPORT), imports growth

(IMPORT). Our estimates are based on annual data for the sample period 1980-2010.

Data are drawn from two main sources: (a) the International Monetary Fund (IMF,

various issues) and the World Development Indicator (World Bank, various issues).

1 We cut Cambodia and Myanmar out of sample data because data are unavailable.


TABLE 2. Trends in GDP growth, exports and imports from 1990 to 2010

Country GDP Growth (%) Exports (% of GDP) Imports (% of GDP)

1990 2000 2010 1990 2000 2010 1990 2000 2010

Brunei 20.95 0.54 17.26 59.14 73.51 63.12 26.74 33.19 23.96

Vietnam 2.84 8.62 11.17 39.01 46.46 67.41 43.91 50.16 80.49

Malaysia 13.34 16.73 23.25 66.83 104.66 83.66 66.27 87.66 69.33

Indonesia 12.79 17.87 31.49 22.58 37.66 22.28 19.34 20.31 19.16

Philippines 3.82 -2.38 18.46 16.74 47.18 25.87 26.54 42.57 27.42

Singapore 23.66 11.11 22.49 136.10 146.50 155.53 156.98 142.76 136.72

Thailand 18.53 0.08 20.93 26.94 56.19 61.26 39.03 50.46 57.89

Laos 19.30 15.33 15.42 7.04 23.86 33.99 16.24 42.06 55.34

Source: IMF and World Bank

The trends in GDP growth, share of exports to GDP and share of imports of

GDP are shown in Table 2. Across ASEAN countries, the trends in GDP growth do not

show any similarly trends. GDP growth in Brunei, Philippines, Singapore, Thailand and

Laos decrease from 1990 to 2000 and increase from 2000 to 2010 while GDP growth in

Vietnam, Malaysia and Indonesia continuously increase from 1990 to 2010. The data

clearly show the highly share of exports and imports on these countries GDP. Compare

to GDP growth, there are upward trend for exports and imports from 1990 to 2010

across all the ASEAN countries under study.

Before estimate the VAR model, we have to check whether each time series

variable is stationary in levels or stationary after first differencing. Two univariate unit

root tests (the augmented Dickey–Fuller (ADF) and Phillips–Perron (PP)) were

examined for each of the variables and were shown in Table 3.

TABLE 3. Tests for unit root

ADF PP Jarque-Bera Prob Skewness Kurtosis

Brunei

GDP -4.811*** -4.811*** 2.345 0.310 0.148 4.572

Exports -6.647*** -6.647*** 0.377 0.828 0.812 3.588

Imports -4.338*** -4.338*** 106.020*** 0.000 -0.787 4.662

Vietnam

GDP -5.088*** -6.330*** 6.608** 0.037 0.105 5.290

Exports -5.505*** -11.965*** 122.658*** 0.000 2.849 11.104

Imports -4.781*** -7.386*** 463.091*** 0.000 4.010 20.497

Indonesia

GDP -6.014*** -6.242*** 47.954*** 0.000 -1.491 8.428

Exports -5.143*** -5.146*** 0.648 0.723 -0.338 2.752

Imports -5.280*** -5.295*** 0.749 0.688 0.320 3.436

Malaysia

GDP -4.707*** -4.652*** 3.227 0.199 -0.795 2.767

Exports -4.977*** -4.989*** 1.076 0.584 -0.421 2.609

Imports -3.898** -3.774** 17.529*** 0.000 -1.524 5.176


ADF PP Jarque-Bera Prob Skewness Kurtosis

Philippines

GDP -4.342*** -4.346*** 1.828 0.401 -0.603 2.915

Exports -3.636** -3.611** 1.034 0.596 -0.439 2.760

Imports -3.700** -3.684** 1.332 0.514 -0.483 2.636

Singapore

GDP -3.241** -3.289** 2.806 0.246 -0.745 2.846

Exports -4.234** -4.116** 0.464 0.793 -0.240 2.626

Imports -4.520*** -4.515*** 2.279 0.320 -0.674 2.932

Thailand

GDP -3.190** -3.251** 14.856*** 0.001 -1.444 4.883

Exports -3.999*** -3.886** 1.220 0.543 -0.214 2.110

Imports -4.173*** -3.913** 0.121 0.941 -0.104 2.767

Loas

GDP -3.959*** -3.758** 3.200 0.202 0.148 4.572

Exports -5.017*** -7.741*** 3.730 0.155 0.812 3.588

Imports -5.365*** -5.286*** 6.547** 0.038 -0.787 4.662

Source: Computation

Notes: ** and *** denotes rejection of the null hypothesis of unit roots for the ADF tests and PP tests at

the 5% and 10% significance levels.

** and *** denotes rejection of the null hypothesis of normality for the Jarque-Bera tests at the 5% and

10% significance levels.

The combination of the unit root tests results (see Table 3) suggest that the GDP

growth, imports growth and exports growth are integrated of order zero (i.e., I(0)) or

stationary at level and so we can construct VAR model without take the differentiate.

Table 3 also provides the normality test for all of variables and the Jarque-Bera on some

of variables reject normality implied that not all marginal of the variables are normal

distribution. Therefore, we can not assume the joint distribution of them is multivariate

normality.

4.2 Estimation of copula-VAR model

The next step is to formulate the appropriate VAR model. The variables in the

VAR models are used on their stationary level. The initial task in estimating the VAR

model is to determine the optimum order of lag length. Moreover, in the real world

economy, GDP, exports and imports always will delay for recognized the external and

internal impact including the impact of changing in value of GDP, exports and imports

on other side of economy were not immediately exist. In order to select the lag length

of VAR model, sequential modified LR test statistic (LR), Akaike information criterion

(AIC), Schwarz information criterion (SIC) and Hannan-Quinn information criterion

(HQ) are used. Table 4 presents selected lag length of each country VAR model.


TABLE 4 Selected Lag Lengths

Country selected lag lengths

Brunei 0

Indonesia 2

Laos 1

Malaysia 0

Philippines 6

Singapore 6

Thailand 0

Vietnam 6

Source: Computation

Table 4 shows that there is no causality among exports, imports and GDP in

three countries (Brunei, Malaysia and Thailand). In the case of Laos, there is 1 lag

length while 2 lag lengths exist in Indonesia. In addition, the proper lag order for

Philippines, Singapore and Vietnam are 6.

After chose the appropriate lag length for each country, we estimate the

parameters in VAR model and copula parameter and results of each country are

separately presented.

1) Long-run relationship among exports, imports and GDP via copula-VAR model

for Indonesia

Table 5 shows that imports and exports are important factors to determined

economic growth in Indonesia at 5 percent significant level or better. The coefficient of

EXPORT(t-1) on GDP growth shows that increase in 1 percent of exports growth will

lead GDP growth increase 0.301 percent. Moreover, the coefficient of IMPORT(t-1) on

GDP growth is 0.758 means the 1 percent increase of imports growth will increase GDP

growth 0.758 percent. This result indicates the impact of imports on GDP is larger than

impact of exports on GDP in the case of Indonesia.

Furthermore, there is relationship between exports growth and imports growth

and Table 5 shows that exports led imports in Indonesia (at 10 percent significant level)

but there is no causal relationship from imports to exports and there is also no causality

from GDP to imports or exports. This result implies that imports and exports policy can

encourage growth in Indonesia and imports are relatively more important than exports

to GDP growth. We can write the relation in the functional form as follow:

GDP growth = f(EXPORT(t-1), IMPORT(t-1))

Imports growth = f (EXPORT(t-2))

Since the joint copula model requires the correct specification of the marginal

models and their probability transforms will be iid uniform(0,1), so we provide the KS

Test for if the probability transforms are uniform(0,1) and Box-Ljung Test for


Autocorrelation. The null hypothesis of KS Test is variable has uniform distribution

and the result from Table 6 rejects the null hypothesis for all 3 margins which implied

that GDP growth, exports growth and imports growth have uniform distribution in the

case of Indonesia. The Ljung–Box tests on the standardized residuals in levels reported

in Table 6 highlight no autocorrelation. These results provide significant evidence that

our marginal models are correctly specified.

TABLE 5 Causality relationship between Exports, imports and GDP in Indonesia

Variables EXPORT IMPORT GDP

Coefficient t-stat Coefficient t-stat Coefficient t-stat

Constant 5.085* 1.919 7.208 1.563 7.785** 2.111

EXPORT(t-1) 0.036 0.138 -0.103 -0.706 0.301** 2.012

IMPORT(t-1) -0.451 -0.996 -0.117 -0.463 0.758*** 2.915

GDP(t-1) 0.242 0.668 -0.082 -0.406 -0.104 -0.499

EXPORT(t-2) -0.104 -0.378 0.247* 1.840 -0.130 -0.774

IMPORT(t-2) 0.378 0.788 -0.177 -0.755 0.154 0.527

GDP(t-2) 0.273 0.712 0.184 0.983 -0.329 -1.405

Log-Likelihood -351.280

AIC 756.559

BIC 794.392

Source: Computation

Notes: *,** and *** denote 10%, 5% and 1% levels of significance respectively.

TABLE 6 testing the assumptions of i.i.d and Test for Autocorrelation

KS test for uniform distribution

Null Hypothesis: Variable has uniform distribution

statistic pValue Hypothesis

Margins of GDP growth 0.0936 0.9448 0 (acceptance)

Margins of exports growth 0.0827 0.9823 0 (acceptance)

Margins of imports growth 0.1351 0.6124 0 (acceptance)

Box-Ljung Test for Autocorrelation

Null Hypothesis: No autocorrelation

Q-Stat pValue Hypothesis




Source: computation

Next, we estimate the copula parameter and we consider pairwise dependence,

so we model bivariate distributions of returns for computational tractability. To each

pair of variables, we fit the following copulas: Normal copula, Clayton's copula,

Rotated Clayton copula, Placket copula, Frank copula, Gumbel copula,and Rotated

Gumbel copula . We fit the copulas to the pairs of standardized residuals, obtained after

fitting VAR models to each returns series, transformed to uniform distribution by their


empirical distribution functions. The copula selection is done on the basis of AIC and

BIC perspective. Table 7 shows the optimal copulas and their estimated parameters.

TABLE 7 Copula correlation matrix

Family Copula

parameter

Kendall’s

tau

GDP and Export Frank 4.817 0.45

GDP and Import rotated Gumbel copula (180 degrees;

“survival Gumbel”) 1.676 0.4

Export and Import condition on GDP Frank 8.002 0.6

Source: Computation

Table 7 shows that, in the case of GDP-export pair and Export-Import pair, the

Frank copula are the most appropriate to model the dependence structure. In the case of

GDP-Import pair is given to the rotated Gumbel copula. The Kendall’s tau shows the

positive dependence of each pair.


for Laos

The result of Table 8 indicates that lag of exports and GDP are important factors

to determined GDP growth in Laos. In addition, there is bidirectional relation between

exports and GDP which support ELG and GLE hypotheses. The result also shows that

exports led imports in Laos. However, all coefficients of imports are insignificant which

can imply unimportant of imports policy. We can write this relation in the functional

form as follow:

GDP growth = f(EXPORT(t-1), GDP(t-1))

Imports growth = f (EXPORT(t-2))

Exports growth = f (GDP(t-1))

Table 8 Causality Relationship between Exports, Imports and GDP in Laos

Variables

EXPORT IMPORT GDP


Constant 31.461*** 3.588 15.906** 2.422 1.653 0.319

EXPORT(t-1) -0.223 -1.288 0.450** 1.649 0.947*** 3.391

IMPORT(t-1) 0.006 0.044 0.019 0.092 0.205 0.981

GDP(t-1) 0.194** 1.898 -0.057 -0.351 0.453*** 2.740

Log-Likelihood 880.028

AIC 917.860

BIC -413.014

Source: Computation

Notes: ** and *** denote 5% and 1% levels of significance respectively.


Next, we provide the KS Test for if the probability transforms are uniform(0,1)

and the null hypothesis of KS Test is variable has uniform distribution and the result

from Table 9 rejects the null hypothesis for all 3 margins which implied that GDP

growth, exports growth and imports growth ,in the case Laos, have uniform distribution.

We also employ the Ljung–Box tests on the standardized residuals in levels reported in

Table 9 and the result highlights no autocorrelation. These results provide significant

evidence that our marginal models are correctly specified and hence copula model will

not be mispecified.

Table 9 testing the assumptions of i.i.d and Test for Autocorrelation













Source: Computation

Table 10 Copula correlation matrix Family Copula parameter Kendall’s tau

GDP and Export Clayton 0.141 0.066

GDP and Import Independence 0.000 0.000

Export and Import

condition on GDP Frank 9.021 0.637

Source: Computation

Table 10 shows that, in the case of GDP-export pair is given to the Clayton

copula and the Export-Import pair is given to the Frank copula while there is no relation

between GDP and Import which support our VAR model. Moreover, the Kendall’s tau

of GDP-export pair and Export-Import pair are positive indicate positive dependence of

each pair.


for Philippines

In the case of the Philippines, the result indicates that exports and imports led

economic growth. Table 11 shows that the elasticity of IMPORT(t-5) is greater than the

elasticity of other variables that and a 1% increase in IMPORT(t-5) leads to a gain in

GDP growth of 2.575%.


Table 11 Causality Relationship between Exports, Imports and GDP in the

Philippines



Constant 5.681** 2.249 2.972 1.096 4.009* 1.915

EXPORT(t-1) -0.035 -0.149 0.698*** 2.687 -0.616** -2.184

IMPORT(t-1) 0.087 0.343 0.224 0.802 0.826*** 2.728

GDP(t-1) 0.323* 1.655 -0.367* -1.707 0.791*** 3.382

EXPORT(t-2) -0.583** -2.012 0.579* 1.859 -0.498 -1.405

IMPORT(t-2) -1.230*** -3.954 1.458*** 4.365 -1.030*** -2.708

GDP(t-2) -0.769*** -3.202 0.859*** 3.328 -0.232 -0.791

EXPORT(t-3) -0.571* -1.842 0.496* 1.626 0.163 0.425

IMPORT(t-3) -0.477 -1.432 0.268 0.819 -0.694* -1.681

GDP(t-3) -0.121 -0.469 -0.039 -0.156 -0.422 -1.324

EXPORT(t-4) 0.419* 1.942 -0.360 -1.441 -0.057 -0.149

IMPORT(t-4) 0.650*** 2.804 -0.508* -1.896 -0.241 -0.583

GDP(t-4) 0.362** 2.022 -0.438** -2.114 0.089 0.278

EXPORT(t-5) -0.218 -0.990 -0.624** -2.399 1.823*** 4.269

IMPORT(t-5) -0.318 -1.346 -0.740*** -2.653 2.575*** 5.618

GDP(t-5) -0.407** -2.230 0.309 1.433 0.580 1.640

EXPORT(t-6) -0.242 -1.131 0.408 1.486 0.557 1.029

IMPORT(t-6) 0.195 0.848 -0.153 -0.518 1.218** 2.100

GDP(t-6) 0.154 0.865 -0.123 -0.541 0.146 0.325


AIC 625.810

BIC 663.643

Source: Computation


For imports growth equation (second column), Table 11 shows exports growth,

GDP growth and its own lag are important factors to determine imports growth. The

results indicate that the elasticity of IMPORT(t-2) is greater than the elasticity of other

variables; and that a 1% increase in IMPORT(t-2) leads to a gain in imports growth of

1.458%. The exports growth is also determined by imports, GDP and its past values.

The result indicates that the elasticity of IMPORT(t-2) is greater than the elasticity of

other variables; and that a 1% increase in IMPORT(t-2) increases exports growth by

1.230%. Therefore, our result supports the ELG, GLE and ILG in Philippines.

From Table 11 above, we can write this relation in the functional form as follow:

GDP growth = f(EXPORT(t-1), IMPORT(t-1), GDP(t-1),

IMPORT(t-2), IMPORT(t-3), EXPORT(t-5),

IMPORT(t-5), IMPORT(t-6))


Imports growth = f (EXPORT(t-1), GDP(t-1), EXPORT(t-2),

IMPORT(t-2), GDP(t-2), EXPORT(t-3), IMPORT(t-4),

GDP(t-4), EXPORT(t-5), IMPORT(t-5))

Exports growth = f(GDP(t-1), EXPORT(t-2), IMPORT(t-2),

GDP(t-2),EXPORT(t-3),EXPORT(t-4),

IMPORT(t-4), GDP(t-4), GDP(t-5))

Next, we provide the KS Test for whether the probability transforms are

uniform(0,1) and the null hypothesis of KS Test is variable has uniform distribution.

The result rejects the null hypothesis for all 3 margins which implied that GDP growth,

exports growth and imports growth, in the case Philippines, have uniform distribution.

We also employ the Ljung–Box tests on the standardized residuals in levels reported in

Table 12 and the result highlights no autocorrelation. These results provide significant

evidence that our marginal models are correctly specified and hence copula model will

not be mis-specified.

Table 13 shows the optimal copulas and their estimated parameters. The

Gaussian copula is appropriate family to capture the dependence structure of GDP-

export pair and GDP-Import pair while Export-Import pair is given to the Clayton

copula. Moreover, the Kendall’s taus of all pairs are positive represent that the ranks of

both variables in each pair increase together.

Table 12 Testing the assumptions of i.i.d and Test for Autocorrelation













Source: Computation


Table 13 Copula correlation matrix

Family Copula parameter Kendall’s tau

GDP and Export Gaussian copula 0.607 0.39

GDP and Import Gaussian copula 0.780 0.54

Export and Import

condition on GDP Clayton copula 1.176 0.39

Source: Computation


for Singapore

In the case of Singapore, the result indicates that exports and imports led

economic growth. In contrast, GDP does determine neither imports nor exports. This

result implies that ELG and ILG but not GLE in Singapore and highlights imports on

GDP growth and exports policy to encourage economic growth.

Moreover, Table 14 shows that the elasticity of imports is greater than the

elasticity of the exports and a 1% increase in imports leads to a gain in GDP growth of

1.941% at 5 percent significant level. We can write this relation in the functional form

as follow:

GDP growth = f(EXPORT(t-2), IMPORT(t-2), GDP(t-2),

EXPORT(t-6), IMPORT(t-6), GDP(t-6))

Imports growth = f (EXPORT(t-5), IMPORT(t-5))

Exports growth = f (EXPORT(t-1), IMPORT(t-1))

Table 14 Causality Relationship between Exports, Imports and GDP in Singapore



Constant 4.087 0.653 4.312 0.651 7.694* 1.667

EXPORT(t-1) 1.273* 1.879 -1.689 -1.517 1.321 1.361

IMPORT(t-1) 1.247* 1.740 -1.758 -1.493 1.387 1.351

GDP(t-1) 0.179 0.359 -0.238 -0.290 0.590 0.824

EXPORT(t-2) 0.390 0.356 0.009 0.006 1.354* 1.690

IMPORT(t-2) 0.262 0.226 0.568 0.377 1.941** 2.291

GDP(t-2) -0.295 -0.365 1.068 1.017 -1.245** -2.108

EXPORT(t-3) 0.061 0.072 -0.329 -0.262 0.518 0.625

IMPORT(t-3) 0.196 0.220 0.074 0.056 -0.180 -0.206

GDP(t-3) -0.626 -1.005 0.577 0.624 0.234 0.383

EXPORT(t-4) 1.189 0.925 -1.310 -1.331 0.462 0.351




IMPORT(t-4) 0.595 0.438 -1.317 -1.265 1.361 0.980

GDP(t-4) 0.223 0.235 -0.616 -0.848 0.803 0.829

EXPORT(t-5) 0.594 0.878 -1.419* -1.724 0.608 0.730

IMPORT(t-5) 0.953 1.332 -1.596* -1.834 0.862 0.978

GDP(t-5) 0.123 0.247 -0.940 -1.549 0.958 1.560

EXPORT(t-6) 1.170 1.411 -0.059 -0.096 -1.273* -1.759

IMPORT(t-6) 1.377 1.571 -0.456 -0.698 -1.586** -2.072

GDP(t-6) 0.860 1.406 -0.282 -0.618 -1.181** -2.212


AIC 540.712

BIC 578.544

Source: Computation


Table 15 presents the KS Test for if the probability transforms are uniform(0,1)



growth, exports growth and imports growth ,in the case Singapore, have uniform

distribution. We also employ the Ljung–Box tests on the standardized residuals in levels

reported in Table 15 and the result highlights no autocorrelation. These results provide

significant evidence that our marginal models are correctly specified.














Source: Computation


Next we estimate the copula correlation and from the AIC and BIC perspective,

the Rotated Gumbel copula was the best among parameter copula to capture the

dependence structure of EXPORT –GDP pair, IMPORT- GDP pair and EXPORT –

IMPORT pair (Table 16). Moreover, the Kendall’s taus of all pairs are positive

suggests that the ranks of both variables in each pair increase together.


Family Copula

parameter

Kendall’s tau

GDP and Export rotated Gumbel copula (180 degrees;


GDP and Import rotated Gumbel copula (180 degrees;


Export and Import

condition on GDP

rotated Gumbel copula (180 degrees;


Source: Computation


for Vietnam

The result of Table 17 indicates that exports and imports are important factors to

determined GDP growth in Vietnam. Moreover, there is bidirectional relation between

imports and GDP which support ILG. In contrast, there is no evidence suggests the

causal direction from GDP to exports. The result also shows that exports led imports

and imports led exports in Vietnam. We can write this relation in the functional form as

follow:

GDP growth = f(IMPORT(t-1),EXPORT(t-2),IMPORT(t-2), EXPORT(t-3),

IMPORT(t-3),GDP(t-3), EXPORT(t-4), GDP(t-4) ,

EXPORT(t-6), IMPORT(t-6))

Imports growth = f (EXPORT(t-2), IMPORT(t-2), GDP(t-5) ,EXPORT(t-6))

Exports growth = f (EXPORT(t-2), EXPORT(t-3), IMPORT(t-3), IMPORT(t-6))


Table 17 Causality Relationship between Exports, Imports and GDP in Vietnam

Variables

EXPORT IMPORT GDP


Constant 14.389** 2.189 4.728 0.563 17.589** 2.068

EXPORT(t-1) 0.505 1.554 -0.483 -1.565 0.050 0.281

IMPORT(t-1) 0.469 1.131 -0.558 -1.417 0.657*** 2.894

GDP(t-1) 0.247 0.588 0.132 0.332 -0.105 -0.456

EXPORT(t-2) 0.814** 2.485 -0.918*** -2.963 0.391* 1.648

IMPORT(t-2) 0.682 1.631 -1.035*** -2.614 0.794*** 2.620

GDP(t-2) 0.295 0.695 -0.003 -0.007 -0.183 -0.597

EXPORT(t-3) 0.889*** 3.331 -0.378 -1.313 1.044*** 4.027

IMPORT(t-3) 1.176*** 3.450 -0.551 -1.496 1.421*** 4.293

GDP(t-3) -0.043 -0.124 -0.597 -1.603 -0.793** -2.366

EXPORT(t-4) -0.245 -0.995 -0.187 -0.621 -0.627** -2.069

IMPORT(t-4) -0.169 -0.537 -0.627 -1.626 -0.452 -1.168

GDP(t-4) 0.393 1.233 0.227 0.582 0.879** 2.244

EXPORT(t-5) 0.270 1.090 0.105 0.345 0.524 1.458

IMPORT(t-5) -0.030 -0.094 0.387 0.998 0.190 0.413

GDP(t-5) -0.188 -0.585 -0.679* -1.728 -0.565 -1.216

EXPORT(t-6) -0.225 -1.126 -0.482* -1.692 -0.468** -1.791

IMPORT(t-6) -0.449* -1.758 0.087 0.240 -0.563** -1.688

GDP(t-6) 0.289 1.116 -0.214 -0.582 0.194 0.573


AIC 763.451

BIC 801.283

Source: Computation


Table 18 presents the KS Test for if the probability transforms are uniform(0,1)



growth, exports growth and imports growth ,in the case Vietnam, have uniform

distribution. We also employ the Ljung–Box tests on the standardized residuals in levels

reported in Table 18 and the result highlights no autocorrelation. These results provide

significant evidence that our marginal models are correctly specified.















Source: Computation

Next we estimate the copula correlation and from the AIC and BIC perspective,

the Frank copula was the best among parameter copula to capture the dependence

structure of EXPORT-GDP and IMPORT-GDP while the Gumbel copula was the best

among parameter copula to capture the dependence structure of EXPORT- IMPORT

(Table 19).


Family Copula parameter Kendall’s tau

GDP and Export Frank Copula 3.767 0.37

GDP and Import Frank Copula 4.977 0.46

Export and Import

condition on GDP Gumbel Copula 3.232 0.69

Source: Computation

4.3 Impulse response function

Next, we will present impulse response function (IRFs) which is tool to analyze

dynamic effects of the system when the model received the impulse. IRFs could provide

more insight into how shocks to exports and imports affect economic growth (and vice

versa). Figure 2-6 provide results for the IRFs for Indonesia, Laos, Philippines,

Singapore and Vietnam, respectively.

Figure 2 the Impulse Response Analysis for Indonesia


According to Figure 2, the first panel shows the impulse response of GDP

growth to exports growth and imports growth for Indonesia. The IRFs shows the

response of GDP to shock on exports and the response of GDP on imports are positive

in the second to seventh period and then the effect gets weaker and become zero after

eight years.

In order to check for reverse causality from GDP to exports and imports the

responses of exports and imports are reported. When the impulse is GDP growth, the

response of exports growth rate is positive and decrease to zero line after ten years.

However, the response of imports growth to GDP shock is insignificantly different from

zero.

Finally, the IRFs shows the response of imports to shock of exports is negative

in the first and second year and then become a positive after four years and the effect

gets weaker after seven years. In contrast, the response of exports to imports is small

negative (around 0-4%) and become zero after eight years.

This finding reinforces the result from VAR analysis which provided support for

the ELG and ILG argument.

Figure 3 the Impulse Response Analysis for Laos

Figure 3 presents the results from IRFs analysis for Laos. First, there is no

evidence in support of ILG as the response of GDP growth due to shocks of imports

growth is not significantly different from zero at all horizons. However, IRFs supports

ELG as a shock of exports has a positive and significant effect on output growth. Figure

3 also shows output growth has a negative impact on exports while there is positive

impact of GDP on imports and the response of exports and imports become fluctuate

around zero line after three years. Finally, there is no evidence appear to confirm

relationship between imports and exports

Therefore, it supports our VAR findings that exports growth causes GDP and

further highlights the significant role of exports in Laos’s economic growth.


Figure 4 the Impulse Response Analysis for Philippines

According to the Figure 4, first panel presents the impact of GDP growth (GDP)

shock, exports growth (EXPORT) shock and imports growth (IMPORT) shock on GDP.

Response of GDP to IMPORT obvious fluctuation whiles the response of GDP to

EXPORT smooth fluctuation and reach to initial equilibrium. The result also shows that

the imports growth (IMPORT) has large effect on GDP growth than exports growth

(EXPORT).

The second panel of Figure 4 shows the impact of GDP growth (GDP) shock,

exports growth (EXPORT) shock and imports growth (IMPORT) shock on exports

growth. Response of EXPORT to IMPORT and GDP obvious fluctuation and the affect

move out from initial equilibrium in the long-run. The result suggests that the IMPORT

has large effect on exports growth than effect of GDP on EXPORT.

The third panel presents the impact of GDP growth (GDP) shock, exports

growth (EXPORT) shock and imports growth (IMPORT) shock on imports growth.

Response of IMPORT to GDP and the response of IMPORT to EXPORT obvious

fluctuation around the zero line and the impact of imports itself have large effect than

GDP growth and exports growth.

Thus, IRFs suggests imports in Philippines have large effect on other variables

than exports growth and GDP growth which highlight important of imports policy to

driving economic growth.

To investigate further the impact of exports growth on GDP growth as compared

to imports growth, we then have used impulse response function to trace the time paths

of GDP in response to a one-unit shock to the variables such as exports growth and

imports growth. The first panel of Figure 5 shows the response of GDP to shock of

exports obvious fluctuation. The effect is negative and the response reach minimum

when the period of response is 4, then the response extent increase. The response of

GDP to shock of imports also fluctuation but the imports growth has less effect than

exports growth.


Figure 5 the Impulse Response Analysis for Singapore

The second panel of Figure 5 shows the response of exports growth to shock of

GDP and imports growth which obvious fluctuate. Moreover, the response of exports

growth to shock of GDP has larger effect than imports growth.

Finally, Figure 5 shows the response of imports to shock of GDP and exports

which varies all time horizons. Moreover, the response of imports growth to shock of

exports has larger effect than GDP growth.

Figure 6 the Impulse Response Analysis for Vietnam

According to the Figure 6, the first panel shows the impact of GDP growth

(GDP) shock, exports growth (EXPORT) shock and imports growth (IMPORT) shock

on GDP. The response of GDP to one S.D. innovations of imports growth is negative

from the first period, then the response reach minimum when the period of response is

4, after that, the response extent increases and reaches to initial equilibrium after ten

years. The response of GDP to exports growth fluctuates around zero line and reaches to

initial equilibrium after ten years. The result shows that the imports growth has large

effect on GDP growth than exports growth.

The second panel of Figure 6 shows the impact of GDP growth (GDP) shock,

exports growth (EXPORT) shock and imports growth (IMPORT) shock on exports


growth. Response of EXPORT to GDP is negative and the response extent increases

when the period of response is 7. The response of EXPORT to IMPORT obvious

fluctuates but moves around zero line. The result shows that the imports growth

(IMPORT) has large effect on exports growth than GDP growth (GDP).

Finally, Figure 6 shows the impact of shock GDP growth (GDP), exports growth

(EXPORT) and imports growth (IMPORT) on IMPORT. Response of IMPORT to GDP

and the response of IMPORT to EXPORT obvious fluctuate and move in the same

direction.

5. Concluding remarks

In this study, Copula-VAR analysis was applied to investigate the causal

relationship among the variables of annual GDP growth, import growth, and export

growth belonging to the period 1980–2010 of ASEAN countries (Brunei, Vietnam,

Malaysia, Indonesia, The Philippines, Singapore, Thailand, and Laos). The

contributions of this paper are the following: 1) export growth and import growth are

included in the model as endogenous variables which previous empirical studies specify

as exogenous variables. 2) We employ copula-VAR model (suggested by Bianchi, et. al

(2010)) and the result suggests that the copula approach are fit to construct the VAR

model in ASEAN case.

In particular, these results indicate that relationship among imports, exports, and

output have different qualitative relationships in each country. Moreover, results suggest

there is a causal relation among imports, exports, and output in Malaysia, Thailand, and

Brunei. In contrast, the study found empirical evidence in support of bi-directional

causal relationship between exports and GDP growth for Laos and The Philippines.

Furthermore, the results of Indonesia, Singapore, and Vietnam support only ELG

hypothesis, not GLE hypothesis. Empirical results also suggest that there is evidence in

support of ILG hypothesis for The Philippines, Indonesia, Singapore, and Vietnam.

This study’s results confirm that the exclusion of imports and the singular focus of

many past studies on merely the role of exports as the engine of growth may be

misleading or lead to incomplete results. Current empirical evidence from selected

ASEAN countries provides empirical support for both ELG and ILG hypothesis, and in

some cases there is also evidence to suggest the impact of import growth as larger than

export growth on GDP growth, which implies the importance of import policy. Thus, it

is reasonable to conclude that for several ASEAN countries, both exports and imports

play a very important role in stimulating economic growth.


ACKNOWLEDGMENT

This work was granted by office of the Higher Education Commission of Thailand. The first

author was supported by a CHE PhD scholarship.

REFERENCES

Aas, K., Czado, C., Frigessi, A., & Bakken, H. (2009). Pair-copula constructions of multiple

dependence. Insurance: Mathematics and Economics, 44(2), 182-198.

ASEAN. (2012). from http://www.aseansec.org/ Awokuse, T. O. (2007). Causality between exports, imports, and economic growth: Evidence

from transition economies. Economics Letters, 94(3), 389-395.

Awokuse, T. O. (2008). Trade openness and economic growth: is growth export-led or import-led? Applied Economics, 40(2), 161-173. doi: 10.1080/00036840600749490

Bedford, T., & Cooke, R. (2001). Probability density decomposition for conditionally dependent

random variables modeled by vines. Annals of Mathematics and Artificial intelligence, 32, 245-268.

Bedford, T., & Cooke, R. (2002). Vines - a new graphical model for dependent random

variables. Annals of Statistics, 10, 1031-1068.

Bhagwati, J. N. (1988). Protectionism. Cambridge: MIT press. Bianchi, C., Carta, A., Fantazzini, D., Giuli, M. E. D., & Maggi, M. (2010). A copula-VAR-X

approach for industrial production modelling and forecasting. Applied Economics,

42(25), 3267-3277. Brechmann, E., & Czado, C. (2011). Extending the CAPM using pair copulas: The Regular

Vine Market Sector model. Submitted for publication.

Çetinkaya, M., & Erdoğan, S. (2010). Var Analysis of the Relation between GDP, Import and

Export: Turkey Case International Research Journal of Finance and Economics (55). Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copula Methods in Finance: Wiley.

Coe, D. T., & Helpman, E. (1995). International R&D spillovers. European Economic Review,

39(5). Frees, E. W., & Valdez, E. A. (1998). Understanding Relationships Using Copulas. North

American Actuarial Journal, 2(1), 1-25.

IMF. (2012). World Economic Outlook Database. Retrieved October, from International Monetary Fund

http://www.imf.org/external/pubs/ft/weo/2009/02/weodata/weoselagr.aspx

Joe H (1996). “Families of m-variate distributions with given margins and m(m-1)/2 bivariate

dependence parameters.” In L Rüschendorf, B Schweizer, MD Taylor (eds.), Distributions with fixed marginals and related topics, pp. 120-141. Institute of

Mathematical Statistics, Hayward.

Joe, H. (1997). Multivariate models and dependence concepts. London: Chapman & Hall. Kababie, J. (2010). Export vs. import -- led growth in Mexico. (Master), ETD Collection for

University of Texas, El Paso. Retrieved from

http://digitalcommons.utep.edu/dissertations/AAI1483868 (Paper AAI1483868) Khan, A. H., Hasan, L., & Malik, A. (1995). Exports, Growth and Causality:An Application of

Co-Integration and Error-correction Modelling: University Library of Munich,

Germany.

Marwah, K., & Tavakoli, A. (2004). The Effect of Foreign Capital and Imports on Economic Growth: Further Evidence from Four Asian Countries: Carleton University, Department

of Economics.

Nelson, R. B. (2006). An Introduction to Copulas. New York: Springer Verlag.


Pistoresi, B., & Rinaldi, A. (2012). Exports, imports and growth New evidence on Italy: 1863–

2004. Explorations in Economic History, 49, 241–254.

Ramos, F. F. R. (2001). Exports, imports, and economic growth in Portugal: evidence from causality and cointegration analysis. Economic Modelling, 18(4), 613-623.

Reppas, P. A., & Christopoulos, D. K. (2005). The export-output growth nexus: Evidence from

African and Asian countries. Journal of Policy Modeling, 27(8), 929-940. Riezman, R. G., Whiteman, C. H., & Summers, P. M. (1996). The Engine of Growth or Its

Handmaiden? A Time-Series Assessment of Export-Led Growth. Empirical Economics,

21(1), 77-110. Rodriguez, F., & Rodrik, D. (1999). Trade Policy and Economic Growth: a Skeptic's Guide to

the Cross-National Evidence: Economic Research Forum.

Sato, S., & Fukushige, M. (2011). The North Korean economy: Escape from import-led growth.

Journal of Asian Economics, 22(1), 76-83. Sims, C. A. (1980). Macroeconomics and Reality. Econometrica, 48, 1-48.

Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges (Vol. 8). Paris:

Publications de l’Institut de Statistique de l’Université de Paris. Thangavelu, S. M., & Rajaguru, G. (2004). Is there an export or import-led productivity growth

in rapidly developing Asian countries? a multivariate VAR analysis. Applied

Economics, 36(10).

Zang, W., & Baimbridge, M. (2012). Exports, imports and economic growth in South Korea and Japan: a tale of two economies. Applied Economics, 44(3), 361-372.


Documents

Chapter 3 Copula-VAR Analysis of the Relation between … · Copula-VAR Analysis of the Relation between GDP, Imports, Exports: ASEAN Case ... and AEC considers the following key